Undergrad Is there a resource which is good questions on quadratic

Click For Summary
SUMMARY

This discussion focuses on resources for exploring quadratic residues within elementary number theory. Key topics include quadratic reciprocity and its applications in cryptography, specifically the quadratic-residue problem. The user seeks significant results rather than basic practice problems. Notable resources shared include PDF handouts and lecture notes from various educational institutions, providing a comprehensive overview of the subject.

PREREQUISITES
  • Understanding of elementary number theory concepts
  • Familiarity with quadratic residues and reciprocity
  • Basic knowledge of cryptographic principles
  • Ability to navigate academic resources and research papers
NEXT STEPS
  • Research "quadratic reciprocity theorem" for deeper insights
  • Explore "quadratic residues in cryptography" for practical applications
  • Study "sphere packing in number theory" for advanced concepts
  • Review lecture notes on "number theory" from academic institutions
USEFUL FOR

Students and educators in mathematics, particularly those focusing on number theory, as well as cryptographers and researchers interested in the applications of quadratic residues.

matqkks
Messages
282
Reaction score
5
I am looking for some interesting questions on quadratic residues. Anyone know of any resources for an elementary number theory course. I am not looking for drill problems to practice but some important results.
 
Mathematics news on Phys.org
Starting with quadratic residue, I arrived at close-packing of spheres within 3 clicks on Wikipedia:
quadratic residue - quadratic reciprocity - cubic reciprocity - sphere packing.
Another example as for many number theoretic results is cryptography: quadratic-rest-problem.
I'm sure there are a lot more results which are probably more sophisticated, too.
 

Similar threads

Undergrad How to introduce quadratic residues?
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Why certain topics in elementary number theory?
  • · Replies 5 ·
Replies
5
Views
2K
MHB Why certain topics in elementary number theory?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What to include in an introduction on number theory?
  • · Replies 1 ·
Replies
1
Views
1K
MHB What to include in an introduction?
  • · Replies 2 ·
Replies
2
Views
2K
MHB How Can Pell's Equation Enhance Elementary Number Theory?
  • · Replies 1 ·
Replies
1
Views
2K
How can Pell's equation be effectively introduced in elementary number theory?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad What resources are there for RSA for the layman?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Questions on Pell's & Non-Linear Diophantine Equations UG Level
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad What are the resources for Pythagorean triples?
  • · Replies 10 ·
Replies
10
Views
2K